Circle Review and Chords
The student will learn that the perpendicular bisector of a chord contains the centre
of a circle and an inscribed angle is twice the measure of a central angle. The
also learn that previous information about circles and geometry will be
combined to learn the new material. The student will also learn that proving
theorems requires using other theorems they have seen previously.
The student will d
emonstrate a basic knowledge of parts of circles and the two new
theorems by playing matching game, working through a work sheet, doing some
paper folding, taking notes and participating in the class and with each other.
The student will
value the skill/ability of remembering circle parts and being able to
find the centre of a circle and its applications. The student will value the ability to
prove geometric theorems.
Topic: Review of circle parts and introduce
chords and angles
Statement: “Today, we'll be starting a new unit on circle geometry. We'll begin by doing a
little bit of review and then jump into new material. The first three exercises of this unit will
be tested on Friday, so we are going to have
to work hard to get everything done.”
Body (85 min.)
Mental Math (8 min.)
Investigation 1 (10 min.)
do questions #1
discuss the result and tangent lines
Matching game and definitions (20 min.)
use the following words:
see attached sheet for the definitions to give for notes
Investigation 2 (15
do question #6 with table partners
do the notes
(give theorem, prove, example)
theorem: the perpendicular from the centre of a circle to a chord bisects the chords (and
Investigation 3 (15
do question #7 with table partners
do the notes (give theorem, prove, exmaple)
the measure of the central angle is equal to twice the measure of the inscribed
angle subtended by the same arc
Assignment and work time (rest of class)
assign 27 (we did #1 already)
D. Conclusion (1
Summary: “We did a really quick review to
day of different circle parts and theorems in
geometry you've seen before. We added a couple of new theorems and modelled how to go
about proving them.”
Assignment: Exercise 27 (except #1)
Did the students show an understanding o
f the material?
Did the paper folding and drawing help the students to visualize the new
Did the students remember a lot of the theorems and circle parts that they
had learned previously?
Did I show an understanding of the material?
s I clear and consice in my explanations?
Did I handle the transitions well between all the different activities?
E. Teaching Aids
overhead and overhead pens
investigation sheet (for students)
sheet with different sized circles (for students and overh
paper folding circles
ruler, compass and protractor
Included within the introduction, body and conclusion.